A Fast Method to Model the Effect of Series Impedance Changes of Transmission Lines on Bus Impedance Matrix

This paper extends Brown's method of Bus Impedance Matrix $(Z_{bus})$ formation to include the case of modifying the series impedance of an existing line. With the conventional Brown's method, modeling such modification requires re-constructing $Z_{bus}$ all over again, which is time-consuming, and redundant if we focus only on specific $Z_{bus}$ elements. Our extended method is based on converting a case of Brown's method (adding a branch between two existing buses) to model direct modification of a branch reactance. We test our improvement on Brown's method on 200-bus, 2383-bus, and 3120-bus systems. Results show that our method rapidly identifies $Z_{bus}$ elements without the need to re-construct $Z_{bus}$ . We also discuss briefly specific benefits of such speed improvement.